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 Keldysh Institute preprints, 2016, 115, 20 pages (Mi ipmp2189)

Extremal measure and external field for two parameters vector equilibrium logarithmic potential problem

M. A. Lapik

Abstract: The vector equilibrium problem of the logarithmic potential theory in external eld with two independent parameters is considered. V. Buyarov and E. Rakhmanov have got explicit formulas that allow to nd the equilibrium measure, and to express the external eld through the family of equilibrium measures supports. These formulas are useful to obtain solutions of the continuum limit Toda lattice by means of the inverse problem method. Our goal is to obtain similar integral formulas for the vector case, where the vector measures are parameterized by the component masses.

Keywords: the inverse problem method, vector equilibrium logarithmic potential theory, equilibrium measures.

 Funding Agency Grant Number Russian Science Foundation 14-21-00025

DOI: https://doi.org/10.20948/prepr-2016-115

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UDC: 517.53+517.9

Citation: M. A. Lapik, “Extremal measure and external field for two parameters vector equilibrium logarithmic potential problem”, Keldysh Institute preprints, 2016, 115, 20 pp.

Citation in format AMSBIB
\Bibitem{Lap16} \by M.~A.~Lapik \paper Extremal measure and external field for two parameters vector equilibrium logarithmic potential problem \jour Keldysh Institute preprints \yr 2016 \papernumber 115 \totalpages 20 \mathnet{http://mi.mathnet.ru/ipmp2189} \crossref{https://doi.org/10.20948/prepr-2016-115} 

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This publication is cited in the following articles:
1. M. A. Lapik, “Formuly vosstanovleniya ravnovesnykh mer dlya zadach ravnovesiya vektornogo potentsiala s ogranicheniyami na mery i vneshnimi polyami”, Preprinty IPM im. M. V. Keldysha, 2018, 203, 16 pp.
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